I want to live my life in a way that won't put him to shame.
"I want to live my life"＝「私は私の人生を生きたい」
"in a way that"＝「～のようなやり方で」
"won't put him to shame."=「彼に恥をかかせないように」
Example in context:
"I admire his way of life, so I would like to also live my life in a way that won't put him to shame."
アメリカ合衆国 
